Previously known methods for cutting various types of plastics such as foam plastic, moulded plastic and other porous materials such as textiles use laser technology which has the drawback that the material is burned. Ultrasound is also used to cut these types of material but has the drawback of being imprecise and "spongy". High-pressure water jets are also used for cutting textiles but produce a messy edge. Electronic beam working also occurs in which electrons are thrown out from a cathode consisting of a tungsten wire, through a hole in an anode, subsequently adjusted magnetically and then concentrated by a magnetic lens. A working temperature of about 6000.degree. C. is reached with this technology and electronic beam working is an unnecessarily complicated technology for the materials for which the present invention is suitable.